Non-coherent multi-symbol-delay differential detector

ABSTRACT

An electronic receiver may generate a differential detection sequence based on a received symbol sequence and based on a m-symbol delayed version of the received symbol sequence, where m is an integer greater than 1. The particular differential detection sequence may be a result of an element-by-element multiplication of the particular received symbol sequence and the conjugate of an m-symbol delayed version of the particular received symbol sequence. The receiver may calculate differential decision metrics based on the differential detection sequence and based on a set of differential symbol sequences generated from the set of possible transmitted symbol sequences. The receiver may generate a decision as to which of a set of possible transmitted symbol sequences resulted in the received symbol sequence, where the decision is based on the differential decision metrics and the set of possible transmitted symbols sequences.

PRIORITY CLAIM

This application is a continuation of U.S. patent application Ser. No.15/006,327, filed Jan. 26, 2016, which is a continuation of U.S. patentapplication Ser. No. 14/602,837 filed Jan. 22, 2015, now U.S. Pat. No.9,246,718, which claims the benefit of U.S. Provisional PatentApplication Ser. No. 61/930,572, filed on Jan. 23, 2014. Each of theabove-referenced applications is hereby incorporated herein by referencein its entirety.

BACKGROUND

Conventional methods and systems for signal detection in electronicreceivers can be too unreliable for some applications. Furtherlimitations and disadvantages of conventional approaches will becomeapparent to one of skill in the art, through comparison of such systemswith some aspects of the present invention as set forth in the remainderof the present application with reference to the drawings.

BRIEF SUMMARY OF THE INVENTION

Systems and methods are provided for non-coherent multi-symbol delaydifferential detection, substantially as shown in and/or described inconnection with at least one of the figures, as set forth morecompletely in the claims.

These and other advantages, aspects and novel features of the presentinvention, as well as details of an illustrated embodiment thereof, willbe more fully understood from the following description and drawings.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 depicts an example transmitter and receiver fit in accordancewith an implementation of this disclosure.

FIG. 2 depicts details of an example receiver in accordance with animplementation of this disclosure.

FIG. 3 is a flowchart of an example process for sequence detection inaccordance with an implementation of this disclosure.

FIG. 4A depicts a physical layer (PL) frame according to the DVB-S2satellite digital broadcast standard.

FIG. 4B depicts an encoder used for generating PL headers according tothe DVB-S2 standard.

FIG. 4C depicts a constellation used for modulating PL header bits fortransmission over the wireless channel according to the DVB-S2 standard.

FIG. 4D depicts an example DVB-2S receiver that is operable to usenon-coherent multi-symbol-delay differential detection in accordancewith aspects of this invention, for detection of DVB-S2 PL headers.

DETAILED DESCRIPTION OF THE INVENTION

As utilized herein the terms “circuits” and “circuitry” refer tophysical electronic components (i.e. hardware) and any software and/orfirmware (“code”) which may configure the hardware, be executed by thehardware, and or otherwise be associated with the hardware. As usedherein, for example, a particular processor and memory may comprise afirst “circuit” when executing a first one or more lines of code and maycomprise a second “circuit” when executing a second one or more lines ofcode. As utilized herein, “and/or” means any one or more of the items inthe list joined by “and/or”. As an example, “x and/or y” means anyelement of the three-element set {(x), (y), (x, y)}. In other words, “xand/or y” means “one or both of x and y”. As another example, “x, y,and/or z” means any element of the seven-element set {(x), (y), (z), (x,y), (x, z), (y, z), (x, y, z)}. In other words, “x, y and/or z” means“one or more of x, y and z”. As utilized herein, the term “exemplary”means serving as a non-limiting example, instance, or illustration. Asutilized herein, the terms “e.g.,” and “for example” set off lists ofone or more non-limiting examples, instances, or illustrations. Asutilized herein, circuitry is “operable” to perform a function wheneverthe circuitry comprises the necessary hardware and code (if any isnecessary) to perform the function, regardless of whether performance ofthe function is disabled or not enabled (e.g., by a user-configurablesetting, factory trim, etc.). The following notation is used in thisdisclosure: {c_(i,k)} is a set of sequences, where the i-th sequence haselements c_(i,k), and i and k are integers; c (bolded) or [c_(k)] is asequence with elements c_(k), where k is an integer; c_(k) is anindividual element of a sequence c or [c_(k)].

FIG. 1 depicts an example transmitter and receiver fit in accordancewith an implementation of this disclosure. The transmitter 100 comprisesa forward error correction (FEC) encoder circuit 102, a modulatorcircuit 104, an analog front-end (AFE) circuit 106, and controlcircuitry 108. The receiver 122 comprises a demodulator and decodercircuit 118, a non-coherent sequence detector circuit 116, an analogfront-end circuit 114, and a control circuitry 120. The transmitter 100and receiver 122 communicate via channel 112, which may be wired,wireless, and/or optical.

Forward error correction encoder 102 accepts data bits and encodes themto generate a signal which is then modulated by modulator 104 resultingin modulated data sequence c_(t), which is one of a set of possibletransmit sequences {c_(i,k)}. The sequence c_(t) is then processed byAFE 106 for transmission onto the channel 112.

Control circuitry 108 executes instructions and generates controlsignals for configuring the other components of the transmitter 100. Inthis regard, control circuitry 108 may determine an encoding andmodulation (e.g., select from among plurality of symbol constellations)to use for transmitting at any given time.

The AFE 114 receives the signal via channel 112 and processes it torecover sequence r. Non-coherent sequence detector 116 processes thereceived sequence r as described below to determine which of thepossible transmit sequences most likely corresponds to r. The mostlikely sequence c_(l) is then output to demodulator and decoder 118,which, then, recovers the transmitted data bits.

Control circuitry 120 executes instructions and generates controlsignals for configuring the other components of the receiver 122. Inthis regard, control circuitry 120 may determine an encoding andmodulation (e.g., select from among plurality of symbol constellations)to use for processing a particular received signal. Which encoding andmodulation is selected may be determined based on a transmitter fromwhich the receiver 122 desires to receive. Which encoding and modulationis to be used with any particular transmitter may be predeterminedand/or determined based on previous communications with the particulartransmitter.

Now referring to FIG. 2, shown are example details of the non-coherentsequence detector 116. The example detector 116 comprises a differentialsequence calculation and storage circuit 202, a differential detectioncircuit 204, a decision metrics calculation circuit 208, and a sequencedecision circuit 206.

The differential sequence calculation and storage circuit 202 isoperable to calculate, and store in memory, a set of differential symbolsequences {d_(i,k) ^(m)} from a set of possible transmit sequences{c_(i,k)} and a selected delay value of m. In the example shown,{c_(i,k)} and m are provided by control circuitry 120. The calculationmay, for example, use equation (4) described below. The controlcircuitry 120 may comprise memory in which the set of possibletransmitted sequences and selected value of m are stored.

The differential detection circuitry 204 is operable to generate adifferential detection sequence y^(m)=[y_(k) ^(m)] based on the receivedsequence r=[r_(k)] and the selected value of m, which in the exampleshown, is provided by the control circuitry 120. The calculation of thedifferential detection sequence may use the equation (2) below.

The decision metrics calculation circuitry 208 is operable to calculatedifferential decision metrics {R_(i) ^(m)} based on the detectionsequence [y_(k) ^(m)] from circuit 204 and the set of differentialsymbol sequences {d_(i,k) ^(m)} from the circuit 202. This calculationmay, for example, be as described by equation (5) below.

The sequence decision circuitry 206 is operable to determine which ofthe possible transmit sequences corresponds to the received signal basedon the set of possible transmit sequences {c_(i,k)} and the calculateddecision metrics {R_(i) ^(m)}.

Operation of the system of FIGS. 1 and 2 will now be described ingreater detail.

Consider a set of L (an integer) modulated data sequences {c_(i,k)},i=1, . . . , L; k=1, . . . N where each sequence encodes log₂(L)information bits to N (an integer) modulated data symbols, drawn from aselected symbol constellation; typically, each sequence is preceded by afixed and known preamble of length M symbols (e.g., for the purpose ofsynchronization between the transmitter and receiver) such that theactual transmitted sequence is c_(t)=[c_(t,−M+1) c_(t,−M+2) . . .c_(t,0) c_(t,1) c_(t,2) . . . c_(t,N)]. Assume that, at a given timeslot, one of these sequences is selected by a transmitter (such astransmitter 100 of FIG. 1) for transmission over a communicationchannel, at symbol rate 1/T_(s). The received symbols corresponding tothe transmitted sequence, in the presence of frequency offset ω_(d),phase noise φ_(k), and additive white Gaussian noise (AWGN) n_(k), aregiven by:r _(k) =c _(k) e ^(j(kω) ^(d) ^(T) ^(s) ^(+φ) ^(k) ⁾ +n _(k) for k=−M+1,. . . ,N.  (1)

A goal at the receiver is to detect the transmitted sequence out of theL possible sequences, given the received symbols r_(k), and retrieve theencoded information bits with minimum probability of error.

Coherent detection on the received data symbols r_(k) could be employedto maximize performance (or, equivalently, minimize the probability oferror) for a given signal to noise ratio (SNR). However, coherentdetection requires accurate tracking of the frequency offset ω_(d) andthe phase noise φ_(k), which is not always feasible or practical,especially in power-limited communication scenarios where the receiverSNR is only a few decibels (dB) or even a fraction of one decibel.Furthermore, such a tracking requirement becomes particularlychallenging if the sequences {c_(i,k)} are short or if they aretransmitted during the acquisition phase of a communication link for thepurpose of receiver synchronization and/or physical later signaling (asis the case with the physical layer (PL) header sequences of the DVB-S2satellite digital broadcast standard, which is described below as anexample application of aspects of this disclosure). Alternatively,non-coherent detection may be used, which is insensitive to frequencyoffset and phase noise. SNR performance of non-coherent detection,however, is inferior compared to coherent detection because of noiseenhancement due to non-coherent processing. Accordingly, aspects of thisdisclosure provide for non-coherent multi-symbol-delay differentialdetection which achieves improved SNR performance (i.e., lowerprobability of error) relative to conventional non-coherent detection,thus closing the gap to coherent detection.

Non-coherent differential detection in accordance with an implementationof this disclosure may comprise, for example, translating a receivedsequence r=[r_(−M+1) r_(−M+2), . . . r₀ r₁ r₂ . . . r_(N)] into adifferential sequence of length N which is formed by conjugatemultiplication of received symbols r_(k) that are not necessarilycontiguous to each other, as is the case with conventional non-coherentdetection, but rather are at delay m≧1 from each other. The delay m maybe chosen so that the minimum distance (e.g., Euclidean distance)between the corresponding differential transmit sequences is maximized(or nearly so, or is, at least, above a determined threshold). This mayprovide improved SNR performance on top of frequency offset and phasenoise immunity. The optimum delay m may be determined based on theproperties of specific FEC code and/or modulation scheme used to formthe original transmit sequences. In an example implementation, delay mcould be a parameter determined at the design phase of the communicationsystem. In another example implementation, delay m may be dynamicallyconfigurable after the receiver has been deployed in the field and evenduring operation of the receiver. For example, the receiver maydynamically choose a mode of operation and the delay m may be selectedbased on the mode currently in use (e.g., based on a feedback loopduring signal reception). Different modes of operation may, for example,correspond to different FEC encoding and/or modulation schemes.Different modes of operation may, for example, be selected for receivingfrom different transmitters. The value of m for a particular transmittermay be predetermined and/or have been determined during previouscommunications with that particular transmitter.

The receiver may, for example, form the m-th delay differentialdetection sequence [y_(k) ^(m)] from the received data symbols r_(k) asfollows:y _(k) ^(m) =r _(k) ·r _(k-m), for k=1, . . . ,N, and 1≦m≦M.  (2)

For sufficiently high SNR and a phase noise process which is assumed tobe linear across N+M symbols, this is can be accurately approximated as:y _(k) ^(m) ≈e ^(j(mω) ^(d) ^(T) ^(s) ^(+Δφ) ^(m) ⁾(c _(k) ·c _(k-m)*+{tilde over (w)} _(k))  (3)

-   -   for k=1, . . . , N, and 1≦m≦M        where {tilde over (w)}_(k) is an additive white Gaussian noise        (AWGN) process with twice the variance of the original AWGN        n_(k), and Δφ_(m) is a constant phase offset only dependent on        m.

Now consider a new set of L (differential) sequences {d_(i,k) ^(m)} thatis constructed from the original set {c_(i,k)}, as follows:d _(i,k) ^(m) =c _(i,k) ·c _(i,k-m)*, for i=1, . . . ,L, and k=1, . . .,N  (4)

This set has its own distance properties, for a given distancedefinition (e.g., Euclidean distance), which are different from those ofthe original set {c_(i,k)}. In an example implementation, m is selectedso that the minimum distance of the set of differential sequences{d_(i,k) ^(m)} is maximized (or is, at least, above a determinedthreshold).

Detecting the original transmitted sequence [c_(k)], for k=1, . . . , Nfrom the received symbols r_(k) is equivalent to detecting thecorresponding m-th delay differential sequence [d_(k) ^(m)] given thedifferential sequence [y_(k) ^(m)] formed by the receiver as shown inequation (2).

To perform this detection, a non-coherent detector in accordance with anexample implementation of this disclosure may construct a set ofdecision metrics by correlating the differential detection sequence[y_(k) ^(m)] with each one of the differential sequences {d_(i,k) ^(m)}and computing the magnitude of this correlation, as follows:R _(i) ^(m)

|Σ_(k=1) ^(N) y _(k) ^(m) ·d _(i,k) ^(m)*|≈|Σ_(k=1) ^(N)(c _(k) ·c_(k-m) *+{tilde over (w)} _(k))·d _(i,k) ^(m)*|  (5)

-   -   for i=1, . . . , L        Then, the non-coherent detector may decide on the l-th sequence        [c_(l,k)] having been transmitted by determining the l-th        differential sequence that yields the maximum decision metric        value, where:

$\begin{matrix}{l = {\arg{\max\limits_{{i = 1},\mspace{11mu}\ldots\mspace{14mu},L}R_{i}^{m}}}} & (6)\end{matrix}$

For a detector in accordance with aspects of this disclosure, immunityto frequency offset and phase noise results from its non-coherent natureand the use of magnitude, which is inherently independent of the phaseinformation, in the above decision metrics. For a detector in accordancewith aspects of this disclosure, robustness in the presence of AWGN isimproved compared to a conventional differential detector obtained forsymbol delay m=1, due to m being chosen to guarantee the best distanceproperties of the differential sequences {d_(i,k) ^(m)}.

FIG. 3 is a flowchart of an example process for sequence detection inaccordance with an implementation of this disclosure. The process beginswith block 302 in which a set of possible transmit sequences {c_(i,k)}is determined (e.g., received by receiver 122 via a control channel orselected by an operator of the receiver 122). In block 304, a value of mis selected for the determined set of possible transmit sequences. Thevalue of m may be selected based, for example, on the type of modulatingand FEC code used for generating the set of possible transmit sequences(which may, for example, be received via a control channel or selectedby an operator of the receiver 122). In block 306, a set of differentialsequences {d_(i,k) ^(m)} is calculated based on the determined set ofpossible transmit sequences and the selected value of m. In block 308, asymbol sequence r is received. In block 310, a differential detectionsequence [y_(k) ^(m)] is generated for the received sequence using theselected value of m. In block 312, a set of decision metrics iscalculated based on the differential detection sequence [y_(k) ^(m)] andthe set of differential sequences {d_(i,k) ^(m)}. In block 314, thetransmit sequence that most likely corresponds to the received symbolsequence is decided based on the differential sequence that yields themaximum decision metric.

An example use of non-coherent differential detection as describedherein is PL header detection in satellite digital broadcast systemsfollowing the DVB-S2 standard. In this regard, the PL header in theDVB-S2 standard is an example of the transmitted sequence c_(t)described above, and thus may be detected using the techniques describedabove. Such an application of those techniques is described withreference to FIGS. 4A-4D.

According to the DVB-S2 standard, a PL header is inserted at thebeginning of each transmitted frame with the purpose of receiversynchronization, and receiver configuration via physical layersignaling. The DVB-S2 frame structure is shown in FIG. 4A. The PL headerconsists of ninety binary symbols. Twenty-six of the symbols arestart-of-frame (SOF) symbols, which are fixed and known. Sixty-four ofthe symbols are physical layer signaling symbols (PLS), each of whichencodes seven bits of information using a generalized (64,7)Reed-Mueller FEC code. Out of these seven information bits, five bitssignal the modulation type and FEC coding rate (mod_cod) used by thetransmitter for data transmission in each one of the S data slots of theframe, one bit signals the frame length type (normal or short), and onebit indicates the presence or absence of pilot symbols in the frame.FIG. 4B depicts an encoder used for generating PL headers according tothe DVB-S2 standard. FIG. 4C depicts the constellation used formodulating the PL header bits, which is an example of a constellationthat may be used by the modulator 104 of FIG. 1.

FIG. 4D depicts an example DVB-2S receiver that is operable to usenon-coherent multi-symbol-delay differential detection in accordancewith aspects of this disclosure, for detection of DVB-S2 PL headers. Areceived signal is digitized via an analog-to-digital converter (A/D)422 and then processed by frequency tracking loop 424 before beingfiltered by an anti-aliasing filter (AAF) 426 and then gain adjusted viadigital automatic gain control (DAGC) circuit 428. The output of DAGC428 is processed by the symbol timing recovery (STR) circuit 430. TheSTR 430 outputs I/Q signals to matched filter (MF) 432. Timing recoveredby STR is conveyed to non-backwards compatible (NBC) frame sync detectorcircuit 440. The MF 432 outputs I/Q signals to carrier tracking loop(CTL) 432, which outputs I/Q signals to equalizer (EQ) 436. The outputof the EQ 436 is then decoded by the forward error correction decoder(FEC) 438. The MF 432 also outputs I/Q signals to physical layer (PL)header detect circuit 442. The PL header detector circuit 442, which isan example implementation of the non-coherent sequence detector 116,implements non-coherent multi-symbol-delay differential detection asdescribed herein to process the I/Q signal from MF 432 using controlssignals from NBC frame sync detect 440 and recover mod_cod information,which is then stored to registers 444.

In operation, the receiver of FIG. 4D receives PL header symbols at rate1/T_(s) in the presence of frequency offset ω_(d), phase noise φ_(k),and AWGN n_(k):r _(k) =c _(k) e ^(j(kω) ^(d) ^(T) ^(s) ^(+φ) ^(k) ⁾ +n _(k), for k=1, .. . , 90.  (7)A conventional non-coherent detector performs differential detectionaccording to the following equation:

$\begin{matrix}{y_{k}^{1} = {{r_{k} \cdot r_{k - 1}^{*}} = {{{\left( {{c_{k}e^{j{({{k\;\omega_{d}T_{s}} + \varphi_{k}})}}} + n_{k}} \right) \cdot \left( {{c_{k - 1}^{*}e^{- {j{({{{({k - 1})}\omega_{d}T_{s}} + \varphi_{k - 1}})}}}} + n_{k - 1}^{*}} \right)} \approx {{c_{k}c_{k - 1}^{*}e^{j{({{\omega_{d}T_{s}} + {\Delta\varphi}})}}} + {n_{k}c_{k - 1}^{*}e^{- {j{({{{({k - 1})}\omega_{d}T_{s}} + \varphi_{k - 1}})}}}} + {n_{k - 1}^{*}c_{k}e^{j{({{k\;\omega_{d}T_{s}} + \varphi_{k}})}}}} \approx {{c_{k}c_{k - 1}^{*}e^{j{({{\omega_{d}T_{s}} + {\Delta\varphi}})}}} + w_{k}}} = {e^{j{({{\omega_{d}T_{s}} + {\Delta\varphi}})}}\left( {{c_{k}c_{k - 1}^{*}} + {\overset{\sim}{w}}_{k}} \right)}}}} & (8)\end{matrix}$The differentially detected signal is insensitive to frequency offsetbut is impaired by approximately two times the noise power. Inaccordance with an example implementation of this disclosure, m-th orderdifferential detection may be applied, instead, for m>1:y _(k) ^(m) =r _(k) ·r _(k-m) *≈e ^(j(mω) ^(d) ^(T) ^(s) ^(+Δφ) ^(m) ⁾(c_(k) c _(k-m) *+{tilde over (w)} _(k))  (9)

-   -   for k=1, . . . , 90

Considering only the last sixty-four PLS code symbols, which encode thephysical layer signaling information, a new (differential) code can begenerated with L codewords, each one corresponding to one of the L PLSoriginal codewords:{d _(i,k-26) ^(m) }={c _(i,k) c _(i,k-m) *},i=1, . . . , L;k=27, . . . ,90  (10)In order to decode mod_cod and frame type, it suffices to determine them-th order differential codeword corresponding to the transmitted PLScodeword, given the differentially detected symbols y_(k) ^(m), k=27, .. . , 90.

In this example, the non-coherent detector may form the followingdecision metrics:

$\begin{matrix}{{R_{i}^{m}\overset{\Delta}{=}{{{\sum\limits_{k = 27}^{90}\;{y_{k}^{m} \cdot d_{i,{k - 26}}^{m^{*}}}}} \approx {{\sum\limits_{k = 27}^{90}\;{\left( {{c_{k} \cdot c_{k - m}} + {\overset{\sim}{w}}_{k}} \right) \cdot d_{i,{k - 26}}^{m^{*}}}}}}}{{i = 1},\ldots\mspace{14mu},{L;}}} & (11)\end{matrix}$and decide that the l-th PLS codeword has been transmitted bydetermining the l-th differential codeword that maximizes the aboveexpression, where:

$\begin{matrix}{l = {\arg{\max\limits_{{i = 1},\mspace{11mu}\ldots\mspace{14mu},L}R_{i}^{m}}}} & (12)\end{matrix}$It is noted that R_(i) ^(m), i=1, . . . , L are independent of thefrequency offset ω_(d) and phase noise φ_(k). In DVB-S2 standard,mod_cod may take on 32 distinct values, from 0 to 31. In addition,assuming that the presence or absence of pilot symbols in the frame isdetermined by the NBC frame sync detector 440 and then signaled to thePL header detector 442 (via a pilot_active control signal, as shown inFIG. 4D), the PL header detector has to decide among L=64 PLS codewords.For a given value of in, the L=64 differential codewords are derivedfrom the respective 64-bit PLS codewords and the last m leastsignificant bits (LSB) of the SOF field according to equation (10), andthey have a length equal to 64. Accordingly, the delay m can take anyvalue between 1 and M=26. A first-order approximation for the PLScodeword (i.e., mod_cod) error probability of the non-coherent PL headerdetector described herein is given by the pair-wise probability betweentwo differential codewords at minimum distance δ_(min), as follows:P _(mod) _(_) _(cod) ≈P _(pair-wise) =Q(√{square root over (SNR·R_(c)·δ_(min))})  (13)where SNR is the signal to noise ratio at the receiver, R_(c) is the PLScoding rate, and Q(x) is the complementary cumulative distributionfunction (CCDF) of the normal Gaussian distribution. Note that theminimum distance δ_(min) is a function of the delay in, and thenon-coherent PL header detector described herein may be configured tominimize the above pair-wise probability by selecting the delay value mthat maximizes δ_(min).

In accordance with an example implementation of this disclosure, anelectronic receiver (e.g., 122) may generate, via differential detectioncircuitry (e.g., 204), a differential detection sequence based on areceived symbol sequence and based on a m-symbol delayed version of thereceived symbol sequence, where m is an integer greater than 1. Theparticular differential detection sequence may be a result of anelement-by-element multiplication of the particular received symbolsequence and the conjugate of an m-symbol delayed version of theparticular received symbol sequence. The receiver may calculate, viadecision metrics calculation circuitry (e.g. 208), differential decisionmetrics based on the differential detection sequence and based on a setof differential symbol sequences generated (e.g., by differentialsequence calculation circuitry 202) from the set of possible transmittedsymbol sequences. The calculating of the differential decision metricsmay be based on the magnitude of the correlation between thedifferential detection sequence and each differential symbol sequencefrom the set of differential symbol sequences. The receiver maygenerate, via sequence decision circuitry (e.g., 206), a decision as towhich of a set of possible transmitted symbol sequences resulted in thereceived symbol sequence, where the decision is based on thedifferential decision metrics and the set of possible transmittedsymbols sequences. The generating of the decision may be based on theparticular transmitted symbol sequence index that results in the maximumdifferential decision metric. The received symbol sequence maycorrespond to a transmitted symbol sequence output by a forward errorcorrection encoder (e.g., 102) and modulator (e.g., 104). A particulardifferential symbol sequence in the set of differential symbol sequencesmay be based on a particular sequence of the set of possible transmittedsymbol sequences and an m-symbol delayed version of the particularsequence of the set of possible transmitted symbol sequences. Theparticular differential symbol sequence may be a result of anelement-by-element multiplication of the particular sequence of the setof possible transmitted symbol sequences and the conjugate of them-symbol delayed version of the particular sequence of the set ofpossible transmitted symbol sequences. The value of m may be selectedbased on a minimum distance of the set of differential symbol sequences.The value of m may be selected based on a mode of operation of theelectronic receiver. The value of m may be selected based on atransmitter from which communications are to be received by theelectronic receiver. The value of m may be selected based on a type ofmodulation and FEC code used for a signal to be received by theelectronic receiver.

Other embodiments of the invention may provide a non-transitory computerreadable medium and/or storage medium, and/or a non-transitory machinereadable medium and/or storage medium, having stored thereon, a machinecode and/or a computer program having at least one code sectionexecutable by a machine and/or a computer, thereby causing the machineand/or computer to perform the processes as described herein.

Accordingly, the present invention may be realized in hardware,software, or a combination of hardware and software. The presentinvention may be realized in a centralized fashion in at least onecomputing system, or in a distributed fashion where different elementsare spread across several interconnected computing systems. Any kind ofcomputing system or other apparatus adapted for carrying out the methodsdescribed herein is suited. A typical combination of hardware andsoftware may be a general-purpose computing system with a program orother code that, when being loaded and executed, controls the computingsystem such that it carries out the methods described herein. Anothertypical implementation may comprise an application specific integratedcircuit or chip.

While the present invention has been described with reference to certainembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the scope of the present invention. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the present invention without departing from its scope.Therefore, it is intended that the present invention not be limited tothe particular embodiment disclosed, but that the present invention willinclude all embodiments falling within the scope of the appended claims.

What is claimed is:
 1. A system comprising: a wireless communicationreceiver comprising: a first delay operable to delay a complex digitalsignal by a first number of samples to generate a first delayed signal,the complex digital signal corresponding to a wireless transmission of asymbol sequence; a second delay operable to delay the complex digitalsignal by a second number of samples to generate a second delayedsignal, wherein the second number is different than the first number; adifferential detector operable to generate a first differential thefirst delayed signal and generate a second differential sequence basedon the second delayed signal; and a decoder operable to estimate thetransmitted symbol sequence based on the first differential sequence andthe second differential sequence.
 2. The system of claim 1, wherein thedifferential detector is operable to generate a product of the complexdigital signal and a conjugate of the first delayed signal and generatea product of the complex digital signal and a conjugate of the seconddelayed signal.
 3. The system of claim 1, wherein the estimatedtransmitted symbol sequence is based on two or more differential symbolsequences generated from a plurality of possible transmitted symbolsequences.
 4. The system of claim 3, wherein one of the first number ofsamples and the second number of samples is selected based on a minimumdistance to the two or more differential symbol sequences.
 5. The systemof claim 3, wherein a particular differential symbol sequence in the twoor more differential symbol sequences is based on a particular sequenceof the plurality of possible transmitted symbol sequences and a delayedversion of the particular sequence of the plurality of possibletransmitted symbol sequences.
 6. The system of claim 5, wherein theparticular differential symbol sequence is a product of the particularsequence of the plurality of possible transmitted symbol sequences and aconjugate of the delayed version of the particular sequence of theplurality of possible transmitted symbol sequences.
 7. The system ofclaim 3, wherein the decoder is operable to correlate the first andsecond differential sequences with the two or more differential symbolsequences.
 8. The system of claim 3, wherein the decoder is operable todetermine a modulation of the transmitted symbol sequence.
 9. A methodcomprising: generating, via a differential detector, two or moredifferential detection sequences based on a received complex signal andbased on two or more delayed versions of the received complex signal,wherein each of the two or more delayed versions of the received complexsignal are delayed by a different number of symbols; and generating, viaa decoder, a decision as to which of a set of possible transmittedsymbol sequences corresponds to the received complex signal, where thedecision is based on the correlation of the two or more differentialdetection sequences with two or more predetermined differential symbolsequences.
 10. The method of claim 9, wherein the two or morepredetermined differential symbol sequences are generated from aplurality of possible transmitted symbol sequences.
 11. The system ofclaim 9, wherein generating the decision comprises generating a minimumdistance between the two or more predetermined differential symbolsequences and the two or more differential detection sequences.
 12. Themethod of claim 9, wherein generating the two or more differentialdetection sequences is based on an element-by-element multiplication ofthe received symbol sequence and a conjugate of the two or more delayedversions of the received symbol sequence.
 13. The method of claim 9,wherein the method comprises determining a modulation of the transmittedsymbol sequence based on the correlation of the two or more differentialdetection sequences with two or more predetermined differential symbolsequences.
 14. A wireless communication receiver, comprising: a variabledelay operable to delay a complex digital signal by a variable number ofsamples to generate one or more delayed signals, the complex digitalsignal corresponding to a wireless transmission of a symbol sequence; adifferential detector operable to generate a differential sequence basedon the complex digital signal and the one or more delayed signals; and adecoder operable to correlate the differential sequence with apredetermined sequence.
 15. The wireless communication receiver of claim14, wherein the differential detector is operable to generate a productof the complex digital signal and a conjugate of the one or more delayedsignals.
 16. The wireless communication receiver of claim 14, whereinthe differential detector is operable to generate a product of the oneor more delayed signals and a conjugate of the complex digital signal.17. The wireless communication receiver of claim 14, wherein anestimated transmitted symbol sequence is based on the correlation of thedifferential sequence with the predetermined sequence.
 18. The wirelesscommunication receiver of claim 14, wherein the variable number ofsymbols is selected based on a minimum distance to the differentialsequence.
 19. The wireless communication receiver of claim 14, whereinthe predetermined sequence is generated from a plurality of possibletransmitted symbol sequences.
 20. The wireless communication receiver ofclaim 14, wherein the decoder is operable to determine a modulation ofthe transmitted symbol sequence.